mechanics of blast loading on the head models

1 23

Biomechanics and Modeling inMechanobiology ISSN 1617-7959 Biomech Model MechanobiolDOI 10.1007/s10237-012-0421-8

Mechanics of blast loading on thehead models in the study of traumaticbrain injury using experimental andcomputational approaches

S. Ganpule, A. Alai, E. Plougonven &N. Chandra

1 23

Your article is protected by copyright and

all rights are held exclusively by Springer-

Verlag. This e-offprint is for personal use only

and shall not be self-archived in electronic

repositories. If you wish to self-archive your

work, please use the accepted author’s

version for posting to your own website or

your institution’s repository. You may further

deposit the accepted author’s version on a

funder’s repository at a funder’s request,

provided it is not made publicly available until

12 months after publication.

Biomech Model MechanobiolDOI 10.1007/s10237-012-0421-8

ORIGINAL PAPER

Mechanics of blast loading on the head models in the studyof traumatic brain injury using experimentaland computational approaches

S. Ganpule · A. Alai · E. Plougonven · N. Chandra

Received: 20 December 2011 / Accepted: 10 July 2012© Springer-Verlag 2012

Abstract Blast waves generated by improvised explosivedevices can cause mild, moderate to severe traumatic braininjury in soldiers and civilians. To understand the interactionsof blast waves on the head and brain and to identify the mech-anisms of injury, compression-driven air shock tubes areextensively used in laboratory settings to simulate the fieldconditions. The overall goal of this effort is to understandthe mechanics of blast wave–head interactions as the blastwave traverses the head/brain continuum. Toward this goal,surrogate head model is subjected to well-controlled blastwave profile in the shock tube environment, and the resultsare analyzed using combined experimental and numericalapproaches. The validated numerical models are then usedto investigate the spatiotemporal distribution of stresses andpressure in the human skull and brain. By detailing the resultsfrom a series of careful experiments and numerical simula-tions, this paper demonstrates that: (1) Geometry of the headgoverns the flow dynamics around the head which in turndetermines the net mechanical load on the head. (2) Bio-mechanical loading of the brain is governed by direct wavetransmission, structural deformations, and wave reflectionsfrom tissue–material interfaces. (3) Deformation and stressanalysis of the skull and brain show that skull flexure andtissue cavitation are possible mechanisms of blast-inducedtraumatic brain injury.

Electronic supplementary material The online version of thisarticle (doi:10.1007/s10237-012-0421-8) contains supplementarymaterial, which is available to authorized users.

S. Ganpule · A. Alai · E. Plougonven · N. Chandra (B)Department of Mechanical and Materials Engineering, Universityof Nebraska–Lincoln, Lincoln, NE, 68588-0656, USAe-mail: [email protected]

Keywords Blast · TBI · Head · Mechanics · Experiments ·Numerical models · FSI

1 Introduction

Improvised explosive devices (IEDs) are weapons frequentlyutilized by insurgents in Iraq and Afghanistan; the explo-sive forces generated from these IEDs can cause traumaticbrain injury (TBI), recognized as the “signature wound” inthese conflicts. The 15 point Glasgow Coma Scale (GCS)(Teasdale and Jennett 1974) defines the severity of a TBIas mild (13–15), moderate (9–12), severe (3–8), and vege-tative state (<3). A recent RAND report estimates that 20 %of the deployed force (total deployed 1.6 million) in theseconflicts potentially suffers from TBI; 40–60 % of theseinjuries are categorized as mild and occur due to explo-sion-induced blast waves (Tanielian and Jaycox 2008). It isspeculated that blast-induced traumatic brain injury (bTBI)is a stress wave dominated phenomenon as opposed to arotational acceleration/deceleration-induced injury, typicallyassociated with the impact injuries commonly encounteredin sports and automobile accidents (Courtney and Courtney2009; Grujicic et al. 2011; Moore et al. 2009; Moss et al.2009; Nyein et al. 2010; Taylor and Ford 2009). Our currentunderstanding of the specific loading pathways and mecha-nisms of blast-induced neurotrauma (BINT) remains incom-plete (Ling et al. 2009). This is particularly detrimental tomedical personnel and patients, since often times bTBI (espe-cially mild and moderate) goes undetected with no diagnosisavailable through neuroradiology or neurophysiology; psy-chological examination may or may not be able to reveal thisailment (Desmoulin and Dionne 2009; Elder and Cristian2009). Repeated exposure to the blast can have cumulativeeffects with irreversible damage to a soldier’s mental capacity

123

Author's personal copy

http://dx.doi.org/10.1007/s10237-012-0421-8

S. Ganpule et al.

(Wang et al. 2011). Detailed knowledge of the mechanics ofblast wave–head interactions is important to the basic under-standing of bTBI. The overall goal of this effort is to under-stand blast wave– head interactions through an integratedexperimental-computational approach. Through this appro-ach, we hope to identify the mechanics of biomechanicalloading of the head and the brain as the blast wave traversesthe head/brain continuum.

While establishing mechanisms of bTBI, it is importantto accurately reproduce field conditions. While blast explo-sions can result in primary (pure blast), secondary (inter-action with shrapnel or fragments), tertiary (impact withenvironmental structures), or/and quaternary (toxic gases)effects (DePalma et al. 2005; Moore et al. 2008), in thiswork, we focus on the effect of primary blast. Furthermore,we consider blast parameters which are likely in the rangeof mild blast traumatic brain injury (mbTBI). For example,when IEDs detonate, at sufficient distances, they propagateas blast waves with a shock front; it is these waves that inter-act with the head/body causing mbTBI. We will refer to theseblast waves with a shock front traveling at supersonic speed,followed by an exponential decay in pressure simply as blastwaves, without the loss of generality. Where the incidence ofmbTBI becomes possible, blast waves are in a planar formand can be characterized as Friedlander waves. Shock tubes,when designed correctly and tested properly, can accuratelysimulate these free-field explosions.

In this work, we use a specially designed compression-driven air shock tube to replicate free-field blast conditionsand expose a surrogate head to a well-defined Friedland-er wave. The interactions between the blast wave and thesurrogate head are modeled using nonlinear finite elementmodel based on Coupled Eulerian Lagrangian formulation;the numerical results are compared with the experimen-tal data for model validation. The various aspects of themechanics of the blast wave–head interactions are analyzedand characterized. In order to understand blast wave–humanhead interactions and analyze how the blast loading affectsthe contents of the brain, experimental boundary conditionsare applied to an anatomically accurate human head-brainnumerical model. Together, experiments and numerical mod-els provide valuable insight into the mechanics of blast wavepropagation and the effect of anatomical features on the sub-sequent biomechanical loading of the head/brain complex.

In Sect. 2, we describe the experimental details of theshock tube, instrumentation/data acquisition methods, andthe constructional details of the surrogate head. In this sec-tion, we also describe the finite element solution method;details of how the anatomically accurate head/brain model isbuilt from MRI; and numerical validation method. In Sect. 3,we present experimental pressure measurements along theshock tube and at five locations on the surface of the surro-gate dummy head and validation of the numerical models.

We also establish the relationship between surface pressureand the pressure [−(σ11 + σ22 + σ33)/3] in the brain/skull.The results are interpreted in terms of pressure wave trans-mission and skull deformation. In Sect. 4, we discuss theinteractions of the hydrodynamic blast flow field on a humanhead in terms of direct and indirect loadings and link the spa-tial-temporal variations of the pressure field in the brain tothe arrival time analysis of the different wave fronts. The keyaspects of the experimental and computational analyses aresummarized in the final section.

2 Methods

2.1 Experiments

Experiments are carried out in the 711×711 mm (28′′ ×28′′)cross-section shock tube designed and tested at the Univer-sity of Nebraska–Lincoln’s blast wave generation facility(Chandra et al. 2011). The four main components of the shocktube are: (1) driver, (2) transition, (3) straight/extension sec-tions (includes test section), and (4) catch tank (Fig. 1a).The driver section contains pressurized gas (e.g., Nitrogenor Helium) which is separated from the transition by sev-eral 0.025- mm-thick Mylar membranes, while the remainingsections contain air at atmospheric pressure and at room tem-perature. The transition section is used to change the cross-section of the tube from a cylinder (driver section) to a square(extension sections); the square section is a design elementto observe events in the test section with high speed videoimaging (600,000 frames per second). Upon membrane rup-ture, a blast wave is generated which expands through thetransition and develops into planar shock-blast waveformin the extension section(s). The test section is strategicallylocated to expose specimens to the blast wave profile of inter-est (Friedlander in this case). Finally, the blast wave exitsthe shock tube and enters the catch tank which absorbs andreleases blast wave energy and reduces the noise intensity.In addition, the catch tank is designed to reduce rarefactionwaves from re-entering the shock tube. The shock tube isdesigned and built such that a fully developed planar shock-blast wave is obtained in the test section located approxi-mately 2,502 mm from the driver end; the total length of theshock tube is 12,319 mm. The cross-sectional dimensions ofthis shock tube is designed such that a head-neck surrogate(e.g., Anthropomorphic Test Dummies (ATD’s) or cadaverhead) experiences a planar blast wave without significantside-wall reflections (Kleinschmit 2011). The planarity ofthe blast wave is verified by pressure measurements acrossthe test section of the shock tube (Kleinschmit 2011).

The realistic explosive dummy (RED) head used as thesurrogate is based on the Facial and Ocular CountermeasUreSafety (FOCUS) head which is modified from the Hybrid

123


Mechanics of blast loading on the head models

Fig. 1 Experimental setup a schematic of the 711 × 711 mm shock tube system b realistic explosive dummy (RED) head with hybrid III neckplaced inside the test section of the shock tube c sensor locations along the midsagittal plane of the RED head

III dummy head, the latter developed for frontal impacts inautomotive accidents. The external geometry of the FOCUSheadform (and hence RED head) is designed to replicate a50th percentile male soldier across the three branches of themilitary Army, Navy, and Air Force (Kennedy 2007). TheRED head consists of a polyurethane skull with an openingfor the brain and cerebrospinal fluid and is attached to theneck through the base plate. The RED head is used in con-junction with the Hybrid III neck in these experiments, andintracranial contents are not included.

The RED head assembly is placed in the test section ofthe shock tube as shown in Fig. 1b and is subjected to frontalblast loading. The shape, overpressure, and duration of theincident blast wave at a given location are known a priori.This is achieved through sample trials in the shock tube, con-ducted without the surrogate head and the neck. Surface pres-sures are measured at different locations on the surface of thehead along the mid-sagittal plane using Kulite pressure sen-sors (model LE-080-250A). The sensor locations are shownin Fig. 1c. The sensing elements can measure the absolutepressure from 0 to 250 psi (0–1.72 MPa) with a nominal cal-ibration of 0.400 mV/psi (58.02 mV/ MPa) using 10 V exci-tation. Incident (side-on) blast wave pressures are measuredat locations A, B, C (Fig. 1a) along the length of the shocktube using PCB pressure gauges (model 134A24).

All pressure sensors utilized in experiments are calibratedunder shock loading conditions using a separate 101 mm (4′′)diameter shock tube and using a flat-topped wave. Accuratecalibrations are achieved by generating precisely controlledshock wave velocities and invoking the Rankine–Hugoniotjump conditions to relate shock wave velocity to shock waveoverpressures.

2.2 Computational modeling

Finite Element (FE) modeling technique is used to simulatethe propagation of a planar blast wave through the shock tube,the interaction dynamics of the blast wave with the head, andthe response of the head/brain to such a loading. In order toeffectively use the experimental results to understand blastwave interactions with the head and its contents, the follow-ing analysis strategy is used:

(a) A finite element based numerical model is developedfor the RED (dummy) head and the shock tube, in con-junction with the Coupled Eulerian Lagrangian (CEL)formulation; here, the experimental data is used tovalidate the computational model in terms of surfacepressure–time (p−t) history on the head and hencemechanical load experienced by the head. The

123


S. Ganpule et al.

agreement between experiments and simulations vali-dates the CEL formulation, solution methodology, theability to capture the complex blast-structure flow fieldvariables (pressure, velocities, and flow separation), aswell as the resulting surface pressures on the structureand the fluid–structure interaction (FSI) effects.

(b) Once the experimental pressure field is validated, themodel is then used to numerically predict the defor-mation and stress fields in the brain of an anatomi-cally accurate human head model developed from theMRI data set. The anatomically accurate human headform is additionally validated (in terms of geometryand material properties) by comparing the numericalmodel against a well-known blunt-impact experimenton human cadavers (Nahum et al. 1977); this assuresthe bio-fidelity of the human head model and the spa-tial–temporal accuracy of kinetic/kinematic variablesin the brain tissue.

2.2.1 FE discretization

The head and neck are modeled with Lagrangian elements,and the air inside the shock tube in which the blast wave prop-agates is modeled with Eulerian elements (Fig. 2). The three-

dimensional human head model is generated from segmen-tation of high resolution MRI data obtained from the VisibleHuman Project (National Institutes of Health 2009). The MRIdata consist of 192 T1-weighted slices of 2562 pixels takenat 1 mm intervals in a male head. The image data are seg-mented into four different tissue types of the head: (1) skin,(2) skull, (3) subarachnoidal space (SAS), and (4) brain. It isnot possible to separately segment cerebrospinal fluid (CSF)and structures such as membranes and bridging veins due tothe resolution of the MRI data, as such they are considereda part of the SAS. The segmentation uses 3D image analysisalgorithm implemented in Avizo�. The interface between allthese tissue types are modeled as tied contact. The segmented3D head model is imported into the meshing software Hyper-Mesh� and is meshed as a triangulated surface mesh. Thevolume mesh is generated from this surface mesh to generate10-noded tetrahedrons. Tetrahedron meshing algorithms arerobust than hexahedral meshing algorithms and can modelcomplex head volumes like brain and SAS faster and eas-ier (Bourdin et al. 2007; Baker 2005; Schneiders 2000).Modified quadratic tetrahedral element (C3D10M) availablein Abaqus� is very robust and is as good as hexahedralelements (Abaqus user’s manual) as far as accuracy of resultsis concerned (Wieding et al. 2012; Cifuentes and Kalbag

Fig. 2 Finite element (FE) discretization

123



Table 1 Finite element (FE)discretization

Component/tissue type No. of nodes No. of elements Type of element

Skin 106,915 54,094 10 Noded tetrahedron

Skull 72,426 36,213 10 Noded tetrahedron

Subarachnoidal space (SAS) 88,783 52,198 10 Noded tetrahedron

Brain 153,750 101,781 10 Noded tetrahedron

Neck 12,691 11,340 8 Noded brick

Eulerian 1,923,390 1,870,960 8 Noded brick (Eulerian formulation)

RED head 74,856 41,057 10 Noded tetrahedron

1992; Ramos and Simões 2006). The use of specialized 3Dimage processing (Avizo�) and meshing software (Hyper-Mesh�) allowed for the development of a geometricallyaccurate FE model. The Eulerian domain (air inside the shocktube) is meshed with eight-noded brick elements, with appro-priate mesh refinement near the regions of solid bodies tocapture fluid–structure interaction (FSI) effects. Parametricstudies on mesh size have been performed and it is found thatmesh size of 3 mm is appropriate to capture flow field aroundthe head (i.e., pressures, velocities) and fluid–structure inter-action (FSI) effects. The mesh convergence is achieved atthis element size; thus, element size of 3 mm is used near theregions of solid bodies and along the direction of blast wavepropagation. Table 1 shows the number of nodes, number ofelements, and element types for each component of the FEmodel. FE discretization is schematically shown in Fig. 2.The RED head is modeled directly from the design (CAD)drawings.

2.2.2 Material models

The skin, skull, and SAS are modeled as linear, elastic, iso-tropic materials with properties adopted from the literature.Elastic properties in general are sufficient to capture the wavepropagation characteristics for these tissue types and thisapproach is consistent with other published works (Chafiet al. 2010; Chen and Ostoja-Starzewski 2010; Grujicic et al.2011; Moore et al. 2009; Moss et al. 2009; Nyein et al. 2010).The brain is modeled with an elastic volumetric response andviscoelastic shear response. The volumetric properties of thebrain are taken from a recent work by Prevost et al. (2011) andthe high frequency shear properties are taken from Nicolleet al. (2005). Owing to the complex anatomical structure andinherent variability associated with biological tissues, sig-nificant uncertainty is reported in material properties of thebrain tissue; a comprehensive review of the brain materialproperties is available in Chavko et al. (2010). We believethat the material parameters for the brain used in this workare the best available combination in terms of proper testingprotocols, the right range of strain rate, and data-reductiontechniques for parameter estimation and applicable to high

on-set rate blast loading conditions. Furthermore, valuesobtained by these two studies agree well with the in vivoMagnetic Resonance Elastography (MRE) measurements(Chavko et al. 2010). Air is modeled as an ideal gas equationof state (EOS). The Mach number of the shock front fromour experiments is approximately 1.4, and hence, the idealgas EOS assumption is acceptable, as the ratio of specificheats do not change drastically at this Mach number. Thematerial properties along with longitudinal wave speeds aresummarized in Table 2.

2.2.3 Solution scheme

The finite element model is solved using the nonlinear tran-sient dynamic procedure with the Euler-Lagrangian couplingmethod (Abaqus�). In this procedure, the governing par-tial differential equations for the conservation of momen-tum, mass, and energy along with the material constitutiveequations and the equations defining the initial and bound-ary conditions are solved simultaneously. Eulerian frame-work allows for the modeling of highly dynamic events (e.g.,shock) which would otherwise induce heavy mesh distor-tion. An enhanced immersed boundary method is used toprovide the coupling between the Eulerian and the Lagrang-ian domains. Here, the Lagrangian region resides fully orpartially within the Eulerian region and provides no-flowboundary conditions to the fluid in the direction normal to thelocal surface. Further, the Eulerian region provides the pres-sure boundary conditions to the Lagrangian region. Thus, acombination of fixed Eulerian mesh and solid–fluid interfacemodeling through the enhanced immersed boundary methodallows for the concurrent simulations of the formation andpropagation of a primary blast wave in a fluid medium andaccounts for the effects of both fluid–structure interactionand structural deformations once the blast wave encountersa solid.

A typical 3D simulation requires about 7 h of CPU time on48 dedicated Opteron parallel processors (processor speed2.2 GHz, 2 GB memory per processor), for an integrationtime of 2.5 ms. The simulation time is selected such that thepeaks due to stress wave action have been established. A time

123


S. Ganpule et al.

Table 2 Material propertiesTissue type Density (kg/m3) Young’s modulus ( MPa) Poisson’s ratio Longitudinal wave

speed, CL (m/s)

(a) Elastic material properties

Skin 1,200 16.7 0.42 188.48

Skull 1,710 5,370 0.19 1856.79

SAS 1,000 10 0.49 413.69

Neck 2,500 354 0.3 436.60

Bulk modulus ( MPa)

Brain 1,040 10 0.4999 98.07

Mode (i) Gi (kPa) βi (s−1)

(b) Viscoelastic material properties of the brain

∞ 0.27 0

1 50 100000

2 6.215 4350

3 2.496 200

4 1.228 5.3

5 1.618 0.0051

Density (kg/m3) Gas constant [J/(kg-K)] Temperature (◦C)

(c) Ideal gas material parameters for airAtmospheric air 1.1607 287.05 27

step of the order of 5 × 10−7 s is used to resolve and capturewave disturbances of the order of 1 MHz, which increasesthe overall computational effort for the total simulation timeof interest.

2.2.4 Loading and boundary conditions

We conducted experiments on the surrogate RED head bysubjecting it to blast in the frontal direction. In order tonumerically reproduce the experiment, there are two possi-ble techniques to impose the boundary conditions: technique(a) Modeling of the entire shock tube, in which driver, tran-sition and extension sections are included in the model sothat events of burst, expansion, and development of a pla-nar of the blast wave are reproduced; technique (b) Partialmodel with experimentally measured (p−t) history is used asthe pressure boundary condition, where the numerical modelcomprises the downstream flow field containing the test spec-imen. Technique (a) is computationally very expensive. Forexample, a full scale simulation of 711 × 711 mm cross-section, 9,880 mm long shock tube (excluding catch tank)with cylindrical to square transition requires about 5 mil-lion eight-noded brick Eulerian elements and takes about 147CPU hours on a dedicated 48 processors. These simulations

reach the limits of computing power in terms of memory andsimulation time. On the other hand, technique (b) requiresabout 1.87 million elements with 7 CPU hours. The pressure,velocity, and temperature profiles obtained using technique(b) matches well with the profiles that are obtained usingfull scale model [technique (a)] at the boundary and down-stream locations (see supplementary material). Hence, tech-nique (b) is capable of capturing the pressure, momentum,and energy of the shock wave and is used here to save timewithout scarifying accuracy. Additional details and compar-ison of the field variables using both these techniques areprovided in the supplementary material. Approach similarto technique (b) has been widely used in shock dynamicsstudies using shock tubes (Honma et al. 2003; Jiang et al.2003; Kashimura et al. 2000). The velocity perpendicular toeach face of Eulerian domain (shock tube) is kept zero inorder to avoid escaping/leaking of air through these faces.This will maintain a planar shock front traveling in the lon-gitudinal direction with no lateral flow. The bottom of theneck is constrained in all six degrees of freedom to avoidrigid body motion. The tied constraint is used between thehead and the neck. The interactions between Eulerian (con-taining air and a propagating blast wave) and Lagrangianregions are treated as fluid–solid interactions using “gen-eral contact” feature (card) in Abaqus�. In general contact,contact constraints are enforced through the penalty method

123



with finite sliding contact formulation. Various contact prop-erty models are available in general contact. In the presentwork, frictionless tangential sliding with hard contact is usedas contact property model. Hard contact defines pressure–overclosure relationship between contacting surfaces. Hardcontact behavior implies that: (1) the surfaces transmit no

contact pressure unless the nodes of the slave surface contactthe master surface, (2) no penetration is allowed at each con-straint location (for penalty constraint enforcement methodused in this work, this condition is only approximated), and(3) there is no limit to the magnitude of contact pressure thatcan be transmitted when the surfaces are in contact.

Fig. 3 Validation of MRI based head model with Nahum’s experimenta head model subjected to Nahum’s impact b locations at which pres-sure comparisons are made against experimental pressures c pressure–

time (p−t) profile comparisons at frontal and occipital locations withexperimentally measured pressures d pressure pattern in the brain att = 5.1 ms

123


S. Ganpule et al.

2.2.5 Validation of the anatomically detailed computationalhuman head model

The anatomically detailed human head model developedfrom the MRI data set is validated using the frontal cadav-eric impact experiment of Nahum et al. (1977). Nahum’sexperiment has become ade-facto standard (Chen and Ostoja-Starzewski 2010; Claessens et al. 1997; Horgan and Gilchrist2003; Kleiven and von Holst 2002; Ruan et al. 1994,Willinger et al. 1999; Zhang et al. 2001b; Zoghi-Moghadamand Sadegh 2009) to validate head/brain numerical models.In Nahum’s experiments, seated stationary cadaver subjectswere impacted at the frontal bone of the skull in the mid-sagittal plane in an anterior–posterior direction by a rigidmass traveling at a constant velocity. They measured intra-cranial pressure at five different locations: (1) the frontalbone adjacent to the impact contact area, (2,3) posterior andsuperior to the coronal and sequamosal sutures, respectively,in the parietal bone, (4) inferior to the lambdoidal suturein the occipital bone and (5) in the occipital bone at theposterior fossa. To simulate Nahum’s experiment, the mea-sured impact force from the cadaver test is applied to themid-frontal area of the numerical human head model in theanterior–posterior direction, in the form of a distributed loadover an area of 1,470 mm2 as shown in Fig. 3a. Pressures aremeasured at points corresponding to the experimental loca-tions described above (Fig. 3b). Comparisons of pressure–time histories between model predictions and experimentalmeasurements (test no 37) are shown in Fig. 3c and pressurepattern predicted by the brain is shown in Fig. 3d. The agree-ment between pressure and time (p−t) profiles at frontaland occipital locations is good. The pressure pattern showstypical coup–countercoup pattern, and pressure varies con-tinuously along the sagittal plane. Similar pattern is reportedby various researcher’s under frontal impact loading condi-tions (e.g., Zhang et al. 2001b). In Nahum’s experiment, headwas rotated forward such that Frankfort anatomical plane wasinclined 45◦ to the horizontal. We conducted one simulationwith this angled impact (case 37), and intracranial pressuresobtained are similar to one obtained with load applied inhorizontal direction (Fig. 3a). The pressure pattern predictedwith angled impact is shown in Fig. 3d. Table 3a shows thecomparison of peak pressures and peak head accelerationsbetween experiments and numerical simulations for varioustest cases of Nahum et al. (1977). Acceleration is based onresultant nodal acceleration at center of mass of the head.The agreement between experiments and numerical simu-lations is good for these test cases as well. The small dif-ferences in peak pressures and peak head accelerations canbe attributed to the discrepancy in geometry and materials,imprecise information on neck boundary conditions and pres-sure transducer locations. In addition, the head model is vali-dated against Trosseille et al. (1992); the results are shown in Ta

ble

3H

ead

mod

elva

lidat

ion

agai

nstt

ests

ofN

ahum

etal

.(19

77)

Test

no.

Inpu

tloa

da(k

N)

Exp

erim

ent

Sim

ulat

ion

%D

iffe

renc

e(a

bsol

ute)

Peak

head

acce

lera

tion

(m/s

2)

Peak

pres

sure

(kPa

)Pe

akhe

adac

cele

ratio

nb

(m/s

2)

Peak

pres

sure

(kPa

)pe

akhe

adac

cele

ratio

n(m

/s2)

Peak

pres

sure

(kPa

)

Fron

tal

Pari

etal

Post

erio

rfo

ssa

Fron

tal

Pari

etal

Post

erio

rfo

ssa

Fron

tal

Pari

etal

Post

erio

rfo

ssa

377.

92,

000

141.

1973

.59

−60.

262,

046.

9415

4.5

61.9

3−6

3.2

2.35

9.43

15.8

54.

87

4114

.84

3,90

042

7.56

188.

52−5

6.80

3,85

741

418

6.34

−59.

311.

103.

171.

164.

43

425.

21,

590

––

−43.

861,

510.

74–

–−4

6.33

4.98

––

5.62

5410

.84

2,34

027

4.51

180.

52−6

4.39

2,39

3.64

247.

1814

1.93

−66.

52.

299.

9621

.38

3.27

aT

hest

iffn

ess

ofth

epa

ddin

gm

ater

iali

nfr

onto

fth

eim

pact

orfo

rca

ses

37,4

1,42

and

54is

notk

now

n.H

ence

,for

case

s41

,42,

and

54,t

hesh

ape

ofth

epr

essu

re–t

ime

profi

leas

that

ofca

se37

isco

nser

ved.

The

pres

sure

puls

eis

scal

edto

mat

chpe

akin

putf

orce

inca

ses

41,4

2an

d54

bA

ccel

erat

ion

isba

sed

onre

sulta

ntno

dala

ccel

erat

ion

atce

nter

ofm

ass

ofth

ehe

ad

123



Tabl

e4

Hea

dm

odel

valid

atio

nag

ains

ttes

tsof

Tro

ssei

lleet

al.(

1992

)

Test

no.

Exp

erim

ent

Sim

ulat

ion

%D

iffe

renc

e(a

bsol

ute)

Peak

pres

sure

(kPa

)Pe

akpr

essu

re(k

Pa)

Fron

tal

Lat

eral

vent

ricl

e3r

dV

entr

icle

Occ

ipita

lPa

riet

alFr

onta

lL

ater

alve

ntri

cle

3rd

Ven

tric

leO

ccip

ital

Pari

etal

Fron

tal

Lat

eral

vent

ricl

e3r

dV

entr

icle

Occ

ipita

lPa

riet

al

MS4

28-1

>60

3025

−13.

512

.472

36.2

230

.9−1

715

.2–

20.7

323

.625

.93

22.5

8

MS4

28-2

a88

4035

−11

10.5

8443

.23

38.5

6−1

3.5

134.

558.

075

10.1

722

.72

23.8

1

aFo

rte

stN

o.M

S428

-2ac

cele

ratio

ntim

ehi

stor

yat

the

cent

erof

mas

sas

repo

rted

inZ

hang

etal

.(20

01a)

isus

ed

Table 4b. Since ventricles are not explicitly modeled in thiswork, the elements in the ventricle region are approximatelyselected based on the knowledge of head anatomy.

3 Results

3.1 Planar blast waves of Friedlander type

Figure 4 shows the measured incident (side-on) pressuresat various locations along the length of the shock tube. Thesensors A, B, C are mounted on the shock tube (markedon Fig. 1a) and located at distances of 1,911, 2,654, and3,124 mm, respectively, from the driver section. Sensor A islocated immediately after the transition section and sensorsB and C are in the test section of the shock tube. It can be seenthat the shape of shock-blast waveform at sensor A has a flattop with a peak overpressure of 0.27 MPa and positive phaseduration of 5.07 ms. The shape of the shock-blast waveformat sensors B and C is of Friedlander type, with peak over-pressures of 0.28 and 0.23 MPa and positive phase durationsof 5.24 and 5.36 ms, respectively.

3.2 Mechanics of blast wave–head interactions

The mechanics of the blast wave–head interactions can bestudied by monitoring the flow field on the surface of thehead. Figure 5a, b, respectively, shows the experimentallymeasured peak pressures and shock wave velocities on theRED (surrogate) head. Incident pressure is measured at sen-sor C, and surface pressures are measured at sensor locationsshown in Fig. 1c. Incident peak overpressure correspondingto sensor C is 0.23 MPa. The peak surface pressure at location1 (forehead) is 0.553 MPa,and thus, the pressure amplifica-tion (the ratio of reflected pressure to incident pressure) is2.40 due to fluid–structure interaction effects. The peak sur-face pressure gradually decreases from locations 1 to 4 as theshock wave traverses the head. The peak pressure at location5 is higher than the locations 3 and 4. The shock wave veloc-ity at incident blast site also increases over free-field velocitydue to fluid–structure interaction effects and then graduallydecreases as the shock wave traverses the head. The shockwave velocity between location 3, 4, and 5 falls below thefree-field shock wave velocity.

3.3 Comparison of experimental and numerical results

Figure 6 shows the surface pressure–time (p−t) profiles cor-responding to sensor locations of Fig. 1c from the shock tubeexperiment and numerical simulation on the RED (surrogate)head. Experimental pressure–time (p−t) profiles are aver-age dover three shots (N = 3). There is a good agreementbetween experiment and numerical simulations, in terms of

123


S. Ganpule et al.

Fig. 4 Blast wave evolution during shock tube experiments

Fig. 5 Mechanics of blast wave head interactions for the surrogatehead a experimentally measured incident (at sensor C) and surfacepressures (corresponding to sensor locations of Fig. 1c) b calculated

incident and surface pressure velocities based on arrival times and dis-tance between sensors

peak pressures, nonlinear decay, and positive phase dura-tions. The simulation is able to capture majority of the fea-tures well, including the shock front rise time, small peaksand valleys, secondary reflections (e.g. sensors 4 and 5). Thearrival times of the experiment are shifted to match arrivaltimes from numerical simulation for ease of comparison ofdifferent features of the pressure–time (p−t) profile. Thereis a slight difference in arrival time between the experimentand the numerical simulation of the order of 0.05 ms (50μs),at most. Difference in arrival time indicates difference inshock wave speed and does not change the pressure andimpulse experienced by the head. The difference in arrivaltime between experiment and simulation can be attributed tothe ideal gas equation of state modeling assumption, mem-brane rupture pattern, friction along the inner wall of theshock tube, and misinterpretation of the vibrations of the

shock tube itself as pressure readings by the pressure sen-sors. Zhu et al. (2012) also found similar differences in arrivaltimes from their experiments and numerical simulations dueto the reasons stated above.

3.4 Relation between surface pressure, cranial andintracranial stress

In the previous section, we validated the numerical modelwith experimental measurements for the surrogate headunder blast loading conditions wherein the geometry of thesurrogate closely matches the anthropometry of a human.In the following sections, the anatomically accurate humanhead model described in Sect. 2.2 is used not only to under-stand the surface interactions but also to study the mechanicsof load transfer to the brain parenchyma.

123



Fig. 6 Comparison of (surface) pressure–time (p−t) history from experiment and numerical simulation on the surrogate RED head. a–e Representssensors 1–5, respectively

When the blast wave impacts the head, it gives rise tovarious types of waves which are defined below.

(i) Surface pressure wave: surface pressure wave is areflected shock wave on the surface of the head. Sur-face pressure wave indicates where the shock front isat a given time. In this work, loading induced by thesurface pressure wave is considered as a “direct load”as the surface pressure wave transmits energy directlyinto the brain.

(ii) Structural wave in the skull: when the blast waveimpacts the head, it gives rise to a stress wave travelingthrough the skin, skull, SAS, and brain. Because ofits acoustic properties, stress wave in the skull travelsmuch faster than in the other soft tissues of the head.Therefore, the stress wave traveling through the skullis monitored in this work and this wave is defined asa structural wave in the skull. The loading inducedby structural wave is considered an “indirect load,” asload is due to structural dynamical deformation.

123


S. Ganpule et al.

As the blast is a moving load, the surface pressure loadsthe skull at different points of time with different intensitiesfrom the front to the back. Thus, there will be sequences ofdirect and indirect loading of the skull and the brain. Thesedirect and indirect loadings cause differential pressure pulsesat various regions of the brain differently.

Table 5 shows the arrival times of the surface pressurewave, structural wave in the skull, and pressure wave in thebrain corresponding to Sects. 1, 2, 3, 4, and 5 of human headmodel as shown in Fig. 7. At Sect. 1, the surface pressurewave arrives first which initiates the structural wave in theskull that in turn initiates pressure wave into the brain. AtSect. 2, the structural wave in the skull arrives slightly ear-lier than the surface pressure wave, since stress wave in theskull travels faster than the surface pressure wave. At Sects. 3,4, and 5, the structural wave in the skull arrives much earlierthan the surface pressure wave. At these sections, the struc-tural wave in the skull establishes a pressure wave in the brain;thus, the pressure wave in the brain also arrives much earlierthan the surface pressure wave. This is obvious from the factthat the longitudinal wave speed in the skull is 1,856.79 m/s(Table 2), whereas the surfacepressure wave around the headtravels at approximately 600 m/s. The free-field blast wavetravels at 450 m/s (Fig. 5b).

Figure 7 shows the surface pressures, pressure in the skull,and pressure in the brain at Sects. 1, 2, 3, and 5 of the humanhead model. As the blast wave encounters the head (Sect. 1),it directly transmits some energy to the brain and at the sametime initiates structural wave in the skull. Once this initia-tion has occurred at Sect. 1, at all other sections, the struc-tural wave arrives earlier than the surface pressure wave, asdepicted in Fig. 7. Thus, except for Sect. 1, the initial bio-mechanical loading of the skull and the brain is governed bythe structural wave traveling in the skull; when the surfacepressure wave arrives at those sections, it causes repressur-ization in the skull and the brain as shown in Fig. 7. Theinitial portion of the pressure–time (p−t) profile at Sect. 5 inthe brain (zoomed in on Fig. 7 and indicated by an asterisk)shows tension (counter-coup pattern), typical of blunt-impactinjuries. When the surface pressure (shock) wave arrives atSect. 5, it induces a compressive load in the brain.

It should also be noted that the pressure profiles of the skulland the brain do not follow surface pressure wave profiles,but instead display oscillating profiles, the potential reasonsfor the oscillations are elaborated in the discussion section.

3.5 Deformation of the skull

The blast wave continues to impose load on various seg-ments of the skull, as it traverses from the front to back. Atthe same time, the stress wave travels through the skull ata speed faster than the blast wave causing complex changesin the shape of the skull. Shape changes of the skull are

Table 5 Arrival times of the surface pressure wave, structural wave inthe skull and pressure wave in the brain at marked sections of Fig. 7

Section Arrival time (ms)

Surface pressurewave

Structural wavein the skull

Pressure wavein the brain

1 0.35 0.37 0.39

2 0.41 0.40 0.43

3 0.58 0.47 0.51

4 0.73 0.52 0.56

5 0.85 0.55 0.59

studied by monitoring transverse displacement of the skullin the mid-axial plane. Figure 8 shows vector plots of theskull (shell, from here on) transverse displacement at vari-ous times. The motion of the shell is considered inward oroutward with respect to its position at an earlier time frame.Initially (t = 0.51 ms), the frontal portion of the shell movesinward and the portion adjacent to it moves outward; at thistime, the stress wave has not propagated into the back of theshell. At slightly later time (t = 0.59 ms), the stress wavepropagates into the back of the shell. At this time, the frontand back portions of the shell moves inward and the cen-ter portion moves outward. As time progresses, the centralportion of the shell starts moving inward (t = 0.69 ms) andeventually a majority of the shell points inward with respectto longitudinal axis (t = 0.82 ms). This is followed by thefront portion of the shell moving outward, while the centerand back portions continue to move inward (t = 0.89 ms).At further times, the center and back portions of the shellalso starts moving outward (t = 1 ms and t = 1.07 ms)and eventually a majority of the shell points outward withrespect to the longitudinal axis (t = 1.43 ms). This is fol-lowed by the entire shell moving inward (with respect toprevious positions) but at a differential rate; the front andthe center portions move faster than the back portion of theshell (t = 1.92 ms and t = 2.14 ms). Then, the shell triesto equilibrate to its original shape (t = 2.36 ms and t =2.50 ms). These vector plots clearly indicate that shell oscil-lates along the longitudinal axis, and differential motion ofvarious portions of the shell causes the flexing (bending)of the shell. In addition to monitoring transverse displace-ment, radial (εrr ) and circumferential (εθθ ) strains are alsoanalyzed at various locations of the shell (plots not shownfor brevity). A local cylindrical coordinate system is used ateach location. It is found that εθθ is ∼10 times higher thanεrr and this confirms that the complex deformations causeflexing of the shell. As the shell stiffness is increased, bothεrr and εθθ are significantly reduced causing a reduction inthe stresses observed in the brain (results not shown for brev-ity).

123



Fig. 7 Relationship between surface pressure, cranial and intracranial stress

3.6 Pressure field inside the brain

One of the important information in studying the effect ofblast wave on the occurrence of TBI is in understanding howpressure varies within the brain as a function of space andtime. Though we have used pressure as the metric to evalu-ate the damage state, other parameters like strain may servethis purpose. However, it is much easier to measure pres-sure in the fluidic brain compared to strain. Figure 9 showsthe pressure profile along the centerline of the brain in themid-sagittal plane. This section is selected as a representa-tive section to understand the effects of loadings due to sur-face pressures and structural dynamical deformations, andthe resulting pressure evolutions in the brain. Various loca-tions at which the pressure history is plotted are marked.Pressure profiles at location 1 and location 6 show typicalcoup (compression)-countercoup (tension) pattern. A tensilewave front (location 6) propagates into the brain from theside opposite to the incident blast side. Thus, there are mul-tiple wave fronts in the brain, a compressive wave front fromthe incident blast side and a tensile wave front from the side

opposite to the incident blast side. This is further confirmedby arrival timing analysis at locations 3 and 5. The tensilewave arrives at location 5 when the compressive wave arrivesat location 3.

Peak pressure at location 1 is ∼0.165 MPa, and this peakis due to the direct transmission of the blast wave into thebrain. The peak is followed by rapid pressure decay; the pres-sure even goes slightly negative before becoming positive.Pressure in the brain at this location (after the first peak) isgoverned by wave reflections from various interfaces. Thepressure profiles at locations 2–6 are governed by competingeffects of the stress wave of the skull, the pressure wave inthe brain, wave reflections from the tissue interfaces, and thesurface pressure wave. The highest positive pressure (com-pressive) of 0.303 MPa is observed at location 2. The speedof the longitudinal wave traveling through the brain withbrain bulk modulus (K) of 10 MPa is 98.07 m/s, as opposedto ∼1,400 m/s with bulk modulus of 2.19 GPa. Thus, for thecase with K = 10 MPa, the longitudinal wave travels muchslower and hence external blast wave–head interactions andreflections from skull boundaries govern the brain intracra-

123


S. Ganpule et al.

Fig. 8 Deformation of the skull

Fig. 9 Pressure field inside the brain

nial pressures. Thus, peak pressure in the brain is observedat location 2 instead of location 1. However, peak pressure inthe SAS (0.45 MPa) which is right behind the skull is higherthan peak pressure (0.303 MPa) at location 2.

Taylor and Ford (2009) observed the highest pressures inthe brain at focal regions located inside the brain due to stresswave action. Grujicic et al. (2011) concluded that multiplereflections give rise to very complex spatial distributions andtemporal evolutions of stresses within the brain from theirnumerical study. Zhu et al. (2010) found highest pressure inthe brain at coup site followed by countercoup, top and cen-ter. They attributed this pattern to complex wave interactionsoccurring near the boundaries. Zhu et al. (2012) used vali-dated egg-shaped surrogate model to study the head responseunder blast loading. Though they have reported highest pres-sure at coup site, from their data (Figure 18 of the reference),it is clear that the initial impulse (i.e., area under p−t curve)is higher for vertex and center regions as compared to couplocation. This corroborates that multiple waves are reach-ing vertex and center regions. All these studies indicate thatintracranial response to the blast wave is governed by thewave interactions. Chen and Ostoja-Starzewski (2010) alsoobserved spherically converging wave pattern at the center ofthe brain. Pressure profiles at locations 3–6 show a significantamount of negative pressure. Maximum negative pressures

123



at locations 3, 4, 5, and 6 are −0.13, −0.16, −0.12, and−0.12 MPa, respectively.

4 Discussion

BINT research is yet to identify the exact mechanism(s) inthe etiology of the trauma, though a few mechanisms havebeen suggested. These include: direct cranial transmission(Bauman et al. 2009; Chavko et al. 2007, 2010; Grujicic et al.2011; Moore et al. 2009; Nyein et al. 2010; Taylor and Ford2009; Zhu et al. 2012), skull flexure (Bolander et al. 2011;Moss et al. 2009), vasospasm (Bhattacharjee 2008; Cernak2005b; Cernak et al. 2001; Courtney and Courtney 2009),linear/rotational acceleration (Krave et al. 2005; Zhang et al.2004), and cavitation (Dogan et al. 1999; Marklund et al.2001; Nakagawa et al. 2009). Any (or all) of these mecha-nisms rely on how the external blast energy is transmitted intothe various regions of the brain, and how different regionsrespond to the mechanical insult in the acute, sub-acute andchronic phases. This work has investigated the first part, inrelating the external blast load to internal pressures by iden-tifying different biomechanical loading pathways.

An important requirement of this study is the abilityto produce repeatable and measurable blast loading condi-tions that can be related to field conditions that cause actualinjury (Cernak 2005a); our blast wave generation facilityhas been designed and tested to meet this need. The place-ment of the specimen (surrogate RED head) is contingentupon the desired blast profile (peak overpressure, duration,and impulse) and is typically achieved in the test section(Sundaramurthy et al. 2012). We have also verified that theblast wave is planar at the test section through measurements(Kleinschmit 2011), as this is an important aspect of repli-cating field conditions.

When the blast wave passes a section of the blast tube, itsstrength is characterized by a pressure gauge (e.g., PCB, Dya-tron, Kulite, Endeveco) measurement mounted on the wallsof the tube and is usually referred to as the side-on pressure.This side-on pressure is the incident pressure pI and mea-sures the static component of the blast wave. Since the veloc-ity component of the pressure wave (dynamic pressure) is notmeasured by pI , this does not represent the total energy ofthe blast. When the blast wave encounters a solid surface, theincident pressure pI is amplified as the high velocity parti-cles of the shock front are brought to rest abruptly, leadingto a reflected pressure pR on the surface of the body. Theamplification factor � = pR

pI(the ratio of reflected pressure

to incident pressure) depends on the incident blast intensity,angle of incidence, mass, and geometry of the object andboundary conditions and can vary by a factor of 2–8 for airshocks (Anderson 2001; Ganpule et al. 2011).

The blast-induced biomechanical force on a loaded body(e.g., rats, dummy, human) depends on the reflected pressureand not on the incident pressure. In this work, we pay particu-lar attention to the measurement of reflected surface pressureand hence the imposed biomechanical load on the body. Thenet biomechanical load F is given by F = ∫

A pRdA =∫A �pI dA. Since the amplification factor � can vary from

2 to 8 and depends on a number of factors, the force variesacross the body even when the incident pressure pI was to bea constant. Recent experimental studies on rats have shownthat surface pressures (and hence the flow field) on the surfaceof a rat head have significant impact on intracranial pressure(Bolander et al. 2011; Leonardi et al. 2011; Sundaramurthy etal. 2012). Thus, in order to understand flow dynamics aroundthe head, surface pressures and wave velocities are monitoredat various locations around the head (Fig. 5). Pressure ampli-fication at the incident blast site (location 1) is � = 2.40 dueto reasons stated above. Pressures and shock wave velocitiesgradually decrease as we move away from the incident blastsite. The shock wave velocity in the top and rear region dropsbelow the free-field velocity. The pressure in the top regionfalls below the incident pressure (� = 0.72 for sensors 3 and4). The sensor on the back side of the head record a higherpressure than those on the top and this pressure is equivalentto incident pressure (� = 1.01 for sensor 5).

In order to assist in the understanding of this complex flowfield, numerical simulations are carried out. From numeri-cal results, it is found that the flow field around the head isgoverned by the geometry of the head. Significant flow sep-aration is observed on the top and sides (90◦) of the head(Fig. 10a). The velocity in the top rear region falls belowthe free-field velocity due to the flow separation effects. Theblast wave traversing the head and the blast wave travers-ing the neck reunite at the back of the head (Fig. 10b). Thisreunion causes an increase in pressure on the back side of thehead. Several other studies (Chavko et al. 2010; Ganpule et al.2011; Mott et al. 2008; Taylor and Ford 2009; Zhu et al. 2012)have shown that geometry of the head plays an important rolein blast wave–head interactions and the biomechanical load-ing of the brain. Our results elucidate that the flow dynamicsstrongly depend on geometry (shape, curvature) and struc-ture (flexural rigidity, thickness) of a specimen and should beconsidered in understanding biomechanical loading pattern.

The impact of the blast wave with the head at the inci-dent blast site causes a direct load and additionally inducesan indirect loading in the form of structural wave travelingthrough the various head components/tissues. The structuralwave through the skull travels faster than any other headcomponent (Table 1) and even faster than the outside sur-face pressure wave. The surface pressure wave in turn trav-els faster than the free-field blast wave due to hydrodynamiceffects. The structural wave of the skull (indirect loading)governs the initial loading of most of the cranial and intra-

123


S. Ganpule et al.

Fig. 10 Flow mechanics around the head as the shock wave traverses the head

cranial contents except the incident blast site region. Whenthe surface pressure wave arrives at given cross-sections, itadds an additional direct load in the form of re-pressuriza-tion (Fig. 7). Thus, a blast wave impact even on a smallarea of the head can trigger the structural wave travelingthrough the skull, which in turn can induce significant bio-mechanical loading to the head in the form of an indirect load.Kleinschmit (2011) subjected a cylindrical shell (mimickingthe skull) filled with a mineral oil (mimicking the brain) tothe blast loading. He measured the surface pressures, sur-face strains on the shell, and pressures in the mineral oil atvarious locations and found that the pressure history in themineral oil is governed by both surface pressures (indicatingexternal blast wave) and surface strains (indicating structuralwave and deformation of the skull); our results support hisfindings. Many of the studies (Bauman et al. 2009; Chavkoet al. 2007, 2010; Grujicic et al. 2011; Moore et al. 2009;Nyein et al. 2010; Taylor and Ford 2009; Zhu et al. 2012)on the bTBI have focused on the direct wave transmissionaspect of BINT. Our results suggest that in addition to thedirect wave transmission effect, structure plays an importantrole in the biomechanical loading of the brain. If this is thecase, then blast mitigation stratagem should not only focus onmitigating the blast wave induced direct loading effects, butshould also take into account these structure-induced indirectloading effects.

The pressure profiles in the skull and the brain deviate fromsurface pressure profiles within a short distance and time.Surface pressure profiles are Friedlander type, whereas pres-sure profiles in the skull and brain show oscillations (Fig. 7).These oscillations in the pressure profiles can be attributed toseveral reasons: (1) Presence of the layered system, that is,skin, skull, SAS, brain; wave travel times in the skin, skull,and SAS along the thickness are 23.87, 2.32, and 10.88μs,respectively, based on longitudinal wave speed. Thus, thepressure response in the skull and the brain, within a short

time, is degraded by reflections from skin–skull, skull–SAS,and SAS–brain interfaces. (2) The 3D nature of the wavepropagation of both structural and surface pressure waves. (3)The surface pressure wave is a moving load; it continuouslydeforms the skull as it traverses the head, these deformationschange the profile.

Any given point, the brain experiences a complex set ofdirect and indirect loadings emanating from different sources(e.g., reflections from tissue interfaces, skull deformation) atdifferent points of time (Fig. 11). These disturbances con-tinuously propagate into the brain as waves. Constructiveand deconstructive interferences of these waves control thepressure–time history in the brain. This is also evident fromthe pressure profiles along the centerline of the mid-sag-ittal plane (Fig. 9). Compressive and tensile waves origi-nate from coup (location 1) and countercoup (location 6)sites. Locations 2–5 show a sinusoidal pattern with a changefrom compression to tension or vice versa, indicating con-structive and deconstructive interferences of various waves.The effects of direct and indirect loading on the brain pres-sure profiles can be delineated only near the surface ofthe brain (Fig. 7 asterisk) and not deep inside the brain(Fig. 9, locations 2–5). Location 2 (Fig. 9) sees the max-imum compressive pressure (0.303 MPa) as the compres-sive wave front from multiple sources reach this locationat the same time. Ward et al. (1980) suggested an intra-cranial pressure injury index to access brain injury sever-ity and the occurrence of the cerebral contusion. Accordingto them, serious brain injury occurs when peak intracranialpressure (compressive) exceeds 0.235 MPa and minor or nobrain injury, for intracranial pressure below 0.173 MPa. Ifthis criterion is applied to our model (Fig. 9), then location2 exceeds the injury threshold and serious brain injury canoccur at location 2. Location 3 records maximum pressure of0.225 MPa; hence, moderate to serious brain injury can occurat location 3.

123



Fig. 11 Wave evolution inside the brain

Skull flexure is proposed as one of the potential mecha-nisms of brain injury (Moss et al. 2009). The transverse vec-tor displacement plots at the mid-axial section of the skullreveals that the skull oscillates (inward, outward and thenequilibrates) about the longitudinal axis at differential ratescausing bending or so-called flexure of the skull (Fig. 8).This is further confirmed by circumferential and radial strainanalysis; circumferential strains are approximately 10 timeslarger than radial strains. Bolander et al. (2011) suggestedskull flexure as a likely candidate for the development ofintracranial pressures from their experimental measurementson rats. A superior rat skull location is identified as the regionof the greatest skull flexure. Thus, geometry and thicknessof the skull are important parameters that govern intracranialpressures. The detailed understanding of how this skull flex-ure affects the intracranial pressure is currently being studied(to quantify direct and indirect loading contributions to theintracranial pressure) and will be reported in future commu-nications.

Tissue cavitation is also proposed as another potentialmechanism (Dogan et al. 1999; Marklund et al. 2001;Nakagawa et al. 2009). Lubock and Goldsmith (1980) used aspherical shell to resemble the head filled with water to accesscavitation theories. They stated that water will form the cavi-ties when exposed to negative pressure below 100 kPa. Loca-tions 3–6 (Fig. 9) exceed this negative pressure threshold;thus, cavitation or microvoid nucleation can occur at theselocations, which belong to occipital and midbrain regions.These negative pressures are due to the interaction of differ-ent indirect structural waves converging on a point.

Effect of bulk modulus on brain pressure: In order to trans-late external mechanical load to tissue level kinetic/kinematicparameters, we need anatomically accurate geometric model,precise description of loading/boundary conditions, and valid

material constitutive equations applicable to loading rangesof interest. While significant progress has been made in theformer two, the latter remains a challenge. Brain as a wholeis very complex with different regions, for example, cerebralcortex, hippocampus, corpus callosum, thalamus, cerebel-lum, and brain stem to name a few, with their own multi-scale anatomical structures with inherent anisotropy. Beinga living matter, the instantaneous behavior can be quite dif-ferent from the observed behavior in the acute and chronicstages due to the biochemical sequelae that are set in motionfollowing the immediate response due to mechanical stimuli.It is no wonder that Chavko et al. (2010) in their excellentreview remark “taken together, the main observation afterfifty years of brain tissue investigation is one of huge dis-parities in the results, especially linked to protocols”. Forexample, a value of 0.83–2,190 MPa has been used for thebulk modulus of brain. These wide variations in part canbe attributed to differences in tissue harvesting procedures,post-mortem testing time, neuroanatomical orientation of thesample, test methods and loading ranges, specimen fixingtechniques, data acquisition and interpretation techniques,and last but not the least the animal sources of the tissueitself. Though it is not the purpose of this paper to examinethe origin of these variations, here we evaluate the effect ofthe value of bulk modulus in the present study.

The bulk modulus in the order of MPa to GPa hasbeen used in different research works. In the lower ranges,Claessens et al. (0.83–83.3 MPa) (Claessens et al. 1997),El Sayed et al. (2.19 MPa) (El Sayed et al. 2008), Nahumet al. (4.5 MPa) (Nahum et al. 1977), Belingardi et al.(5.625 MPa) (Belingardi et al. 2005), Zoghi-Moghadam andSadegh (50 MPa) (Zoghi-Moghadam and Sadegh 2009) haveused values in MPas. Values of the order of GPa havebeen used by Zhang et al. (2.19 GPa) (Zhang et al. 2001a),

123


S. Ganpule et al.

Fig. 12 Pressure field inside the brain for K = 2.19 GPa

Willinger et al. [2.19 GPa, but the bulk modulus of subarach-noid space used was low (0.21 MPa)] (Willinger et al. 1999),Takhounts et al. (0.56 GPa) (Takhounts et al. 2008, 2003),Kleiven and von Holst (2.1 GPa) (Kleiven and von Holst2002). Many of these values were obtained as fitting param-eters in computational simulations to match available exper-imental results of Nahum et al. (1977), though some papersquote previous experimental data (McElhaney et al. 1973;Stalnaker 1969). Ruan et al. (1994) recommended value ofbulk modulus between 21.9 and 219 MPa based on paramet-ric studies on three-dimensional finite element head model.Nahum et al. (1977), Ruan et al. (1994), Khalil and Viano(1982), and Nusholtz et al. (1987) have suggested that com-pressibility of brain tissue is critical in accurately predictingintracranial response. The present work uses a bulk mod-ulus of 10 MPa, based on a recent experimental work byPrevost et al. (2011) conducted on porcine gray/white tis-sue in unconfined compression under loading/unloading fol-lowed by stress relaxation under three different strain rates.The volumetric compliance of the tissue is assessed usingvideo extensometry techniques. The data are combined withexperiments of Pervin and Chen (2009) to obtain parametersthat are valid over a wide strain rate range (0.01–3,000 s−1);the authors suggest that this model is suitable for use underimpact, blast, and shock loading conditions.

Strain rate for the brain tissue in our simulations is 500 s−1

(as opposed to 40 s−1 obtained by simulating case 37 ofNahum et al. (1977) impact experiments). This maximumstrain rate is observed in frontal region. However, for thesake of understanding the role of the value of bulk modulusin the present study, an additional simulation is conductedwith a value of 2.19 GPa and the results are shown in Fig. 12.From the Fig. 12, it can be seen that the higher bulk modu-lus value leads to increase in peak values of brain pressureas well as shift in the location of maximum peak, due tochange in stress magnitudes and wave speeds. The compres-sive wave front traverses the brain tissue much faster (as canbe seen from arrival times) due to change in wave speed andhence effectively erodes the tensile wave front. However,even when bulk modulus value of GPa is used in the simu-lations, the broader conclusions drawn in the paper remain

unaffected. From the foregoing discussions, it is clear thatthe value of bulk modulus affects the pressure pattern. Sincethere is uncertainty in the experimental measuring methodsin the evaluation of bulk modulus, these results should beinterpreted carefully with this variability in mind.

5 Summary and conclusions

Blast-induced traumatic brain injury is the most prevalentmilitary injury in Iraq and Afghanistan, yet little is knownabout how blast waves induce brain injury. A comprehen-sive knowledge of the loading mechanics of brain tissue isimportant in understanding the pathophysiology of BINT aswell as in designing effective mitigation strategies for blastwaves. In this work, blast wave–head interactions are studiedon dummy and real head models for a frontal blast scenario,using a combined experimental and numerical approach. Thecritical factors in biomechanical loading of the head-braincomplex are identified by understanding the loading path-ways of the blast wave from the external surface of the headto the brain. Though this work is primarily focused on planarFriedlander waves (which is important to establish/under-stand mechanisms), the basic understanding and the resultsare valid for other complex scenarios of explosion inducedblast waves encountered in the field.

Some of the key findings of this work are:

• When a shock-blast wave encounters the head-neck, theflow field around the head is not uniform. Surface pres-sures and velocities on the surface of the head at incidentblast site are amplified due to fluid–structure interactionsand hydrodynamic effects.

• Geometry of the head governs the flow dynamics aroundthe head, flow separation and flow reunion; these in turndetermine surface pressures and velocities. Surface pres-sures and shock wave velocities gradually decrease asthe blast wave traverses the head. On the back side of thehead, a slight increase in surface pressure is observed dueto flow reunion.

• Deformation and stress fields in the brain are governedby the surface pressure (external shock) wave and the

123



structural wave of the skull in terms of direct and indi-rect loadings, respectively. Structural response plays animportant role in the biomechanical loading of the brain.

• Skull deforms in a complex manner at different rates as itoscillates around the brain. These complex deformationsare governed by the direct and indirect loadings of theblast that vary with time and can cause flexure (bending)of the skull.

• Pressures in the brain are governed by constructive anddeconstructive interferences of various waves reachinga given location in the brain at a given time. It is onlypossible to delineate effects of direct and indirect load-ings near the surface of the brain and not deep inside thebrain.

• Occipital and midbrain regions of the brain show a signif-icant amount of negative pressure. Thus, the possibilityof cavitation as a potential brain injury mechanism needsto be evaluated.

Acknowledgments The authors acknowledge the financial supportprovided by the U.S. Army Research Office for the project on “Army-UNL Center for Trauma Mechanics”, Contract No. W911NF-08-1-0483(Project Manager: Larry Russell, P.I: Namas Chandra). The authorsthank Ruqiang Feng, Aaron Holmberg of University of Nebraska–Lin-coln (UNL) for many useful discussions.

References

Anderson J (2001) Fundamentals of aerodynamics. McGraw-Hill, NewYork

Baker TJ (2005) Mesh generation: art or science. Prog Aerosp Sci41(1):29–63. doi:10.1016/j.paerosci.2005.02.002

Bauman RA, Ling G, Tong L, Januszkiewicz A, Agoston D,Delanerolle N, Kim Y, Ritzel D, Bell R, Ecklund J, ArmondaR, Bandak F, Parks S (2009) An introductory characterizationof a combat-casualty-care relevant swine model of closed headinjury resulting from exposure to explosive blast. J Neurotrauma26(6):841–860. doi:10.1089/neu.2008.0898

Belingardi G, Chiandussi G, Gaviglio I (2005) Development and val-idation of a new finite element model of human head. In: 19thInternational technical conference on the enhanced safety of vehi-cles, Washington, DC

Bhattacharjee Y (2008) Neuroscience—shell shock revisited: solvingthe puzzle of blast trauma. Science 319(5862):406–408. doi:10.1126/science.319.5862.406

Bolander R, Mathie B, Bir C, Ritzel D, Vandevord P (2011) Skull flex-ure as a contributing factor in the mechanism of injury in the ratwhen exposed to a shock wave. Ann Biomed Eng 39(10):2550–2559. doi:10.1007/s10439-011-0343-0

Bourdin X, Beillas P, Petit P, Troseille X (2007) Comparison of tetrahe-dral and hexahedral meshes for human finite element modelling: anapplication to kidney impact. In: 20th Enhanced safety of vehiclesconference: innovations for safety: opportunities and challenges

Cernak I (2005a) Animal models of head trauma. NeuroRX 2(3):410–422. doi:10.1602/neurorx.2.3.410

Cernak I (2005b) Penetrating and blast injury. Restor Neurol Neurosci23(3):139–143

Cernak I, Wang ZG, Jiang JX, Bian XW, Savic J (2001) Ultrastruc-tural and functional characteristics of blast injury-induced neuro-

trauma. J Trauma-Injury Infect Crit Care 50(4):695–706. doi:10.1097/00005373-200104000-00017

Chafi M, Karami G, Ziejewski M (2010) Biomechanical assessment ofbrain dynamic responses due to blast pressure waves. Ann BiomedEng 38(2):490–504. doi:10.1007/s10439-009-9813-z

Chandra N, Holmberg A, Feng R (2011) Controlling the shape of theshock wave profile in a blast facility, U.S. Provisional patent appli-cation no. 61542354

Chatelin S, Constantinesco A, Willinger R (2010) Fifty years of braintissue mechanical testing: from in vitro to in vivo investigations.Biorheology 47(5–6):255–276. doi:10.3233/bir-2010-0576

Chavko M, Koller WA, Prusaczyk WK, McCarron RM (2007) Mea-surement of blast wave by a miniature fiber optic pressure trans-ducer in the rat brain. J Neurosci Methods 159(2):277–281. doi:10.1016/j.jneumeth.2006.07.018

Chavko M, Watanabe T, Adeeb S, Lankasky J, Ahlers ST,McCarron RM (2010) Relationship between orientation to a blastand pressure wave propagation inside the rat brain. J NeurosciMethods 195(1):61–66. doi:10.1016/j.jneumeth.2010.11.019

Chen Y, Ostoja-Starzewski M (2010) MRI-based finite element model-ing of head trauma: spherically focusing shear waves. Acta Mech213(1–2):155–167. doi:10.1007/s00707-009-0274-0

Cifuentes AO, Kalbag A (1992) A performance study of tetrahedraland hexahedral elements in 3-D finite element structural analy-sis. Finite Elem Anal Des 12(3–4):313–318. doi:10.1016/0168-874x(92)90040-j

Claessens M, Sauren F, Wismans J (1997) Modeling of the human headunder impact conditions: a parametric study. In: Proceedings of41st stapp car crash conference, pp 315–328

Courtney AC, Courtney MW (2009) A thoracic mechanism of mildtraumatic brain injury due to blast pressure waves. Med Hypothe-ses 72(1):76–83. doi:10.1016/j.mehy.2008.08.015

DePalma RG, Burris DG, Champion HR, Hodgson MJ (2005) Blastinjuries. N Engl J Med 352(13):1335–1342. doi:10.1056/NEJMra042083

Desmoulin GT, Dionne JP (2009) Blast-induced neurotrauma: surro-gate use, loading mechanisms, and cellular responses. J Trauma-Injury Infect Crit Care 67(5):1113–1122. doi:10.1097/TA.0b013e3181bb8e84

Dogan A, Rao AM, Baskaya MK, Hatcher J, Temiz C, Rao VLR,Dempsey RJ (1999) Contribution of polyamine oxidase to braininjury after trauma. J Neurosurg 90(6):1078–1082. doi:10.3171/jns.1999.90.6.1078

El Sayed T, Mota A, Fraternali F, Ortiz M (2008) Biomechanics oftraumatic brain injury. Comput Methods Appl Mech Eng 197(51–52):4692–4701. doi:10.1016/j.cma.2008.06.006

Elder GA, Cristian A (2009) Blast-related mild traumatic brain injury:mechanisms of injury and impact on clinical care. Mount Sinai JMed 76(2):111–118. doi:10.1002/msj.20098

Ganpule S, Gu L, Alai A, Chandra N (2011) Role of helmet in themechanics of shock wave propagation under blast loading condi-tions. Comput Methods Biomech Biomed Eng 1–12. doi:10.1080/10255842.2011.597353

Grujicic M, Bell W, Pandurangan B, Glomski P (2011) Fluid/structureinteraction computational investigation of blast-wave mitigationefficacy of the advanced combat helmet. J Mater Eng Perform20(6):877–893. doi:10.1007/s11665-010-9724-z

Honma H, Ishihara M, Yoshimura T, Maeno K, Morioka T (2003) Inter-ferometric CT measurement of three-dimensional flow phenomenaon shock waves and vortices discharged from open ends. ShockWaves 13(3):179–190. doi:10.1007/s00493-003-0206-1

Horgan TJ, Gilchrist MD (2003) The creation of three-dimensionalfinite element models for simulating head impact biomechanics.Int J Crashworthiness 8(4):353–366. doi:10.1533/ijcr.2003.0243

Jiang Z, Wang C, Miura Y, Takayama K (2003) Three-dimensionalpropagation of the transmitted shock wave in a square cross-

123


http://dx.doi.org/10.1016/j.paerosci.2005.02.002

http://dx.doi.org/10.1089/neu.2008.0898

http://dx.doi.org/10.1126/science.319.5862.406

http://dx.doi.org/10.1126/science.319.5862.406

http://dx.doi.org/10.1007/s10439-011-0343-0

http://dx.doi.org/10.1602/neurorx.2.3.410

http://dx.doi.org/10.1097/00005373-200104000-00017

http://dx.doi.org/10.1097/00005373-200104000-00017

http://dx.doi.org/10.1007/s10439-009-9813-z

http://dx.doi.org/10.3233/bir-2010-0576

http://dx.doi.org/10.1016/j.jneumeth.2006.07.018



http://dx.doi.org/10.1007/s00707-009-0274-0

http://dx.doi.org/10.1016/0168-874x(92)90040-j

http://dx.doi.org/10.1016/0168-874x(92)90040-j

http://dx.doi.org/10.1016/j.mehy.2008.08.015

http://dx.doi.org/10.1056/NEJMra042083

http://dx.doi.org/10.1056/NEJMra042083

http://dx.doi.org/10.1097/TA.0b013e3181bb8e84

http://dx.doi.org/10.1097/TA.0b013e3181bb8e84

http://dx.doi.org/10.3171/jns.1999.90.6.1078

http://dx.doi.org/10.3171/jns.1999.90.6.1078

http://dx.doi.org/10.1016/j.cma.2008.06.006

http://dx.doi.org/10.1002/msj.20098

http://dx.doi.org/10.1080/10255842.2011.597353

http://dx.doi.org/10.1080/10255842.2011.597353

http://dx.doi.org/10.1007/s11665-010-9724-z

http://dx.doi.org/10.1007/s00493-003-0206-1

http://dx.doi.org/10.1533/ijcr.2003.0243

S. Ganpule et al.

sectional chamber. Shock Waves 13(2):103–111. doi:10.1007/s00193-003-0197-y

Kashimura H, Yasunobu T, Nakayama H, Setoguchi T, MatsuoK (2000) Discharge of a shock wave from an open end of a tube.J Thermal Sci 9(1):30–36. doi:10.1007/s11630-000-0042-x

Kennedy EA (2007) The development and validation of a biofidel-ic synthetic eye for the facial and ocular countermeasure safety(FOCUS) headform. PhD dissertation, Virginia Polytechnic Insti-tute and State University, Blacksburg

Khalil TB, Viano DC (1982) Critical issues in finite element modelingof head impact. In: Proceedings of 26th stapp car crash conference,SAE Paper No 821150

Kleinschmit NN (2011) A shock tube technique for blast wave sim-ulation and studies of flow structure interactions in shock tubeblast experiments. Master’s thesis, University of Nebraska–Lin-coln, Lincoln

Kleiven S, von Holst H (2002) Consequences of head size followingtrauma to the human head. J Biomech 35(2):153–160. doi:10.1016/s0021-9290(01)00202-0

Krave U, Höjer S, Hansson H-A (2005) Transient, powerful pressuresare generated in the brain by a rotational acceleration impulse tothe head. Eur J Neurosci 21(10):2876–2882. doi:10.1111/j.1460-9568.2005.04115.x

Leonardi AD, Bir CA, Ritzel DV, VandeVord PJ (2011) Intracranialpressure increases during exposure to a shock wave. J Neurotrauma28(1):85–94. doi:10.1089/neu.2010.1324

Ling G, Bandak F, Armonda R, Grant G, Ecklund J (2009) Explosiveblast neurotrauma. J Neurotrauma 26(6):815–825. doi:10.1089/neu.2007.0484

Lubock P, Goldsmith W (1980) Experimental cavitation studies in amodel head–neck system. J Biomech 13(12):1041–1052. doi:10.1016/0021-9290(80)90048-2

Marklund N, Clausen F, Lewen A, Hovda DA, Olsson Y, HilleredL (2001) Alpha-Phenyl-tert-N-butyl nitrone (PBN) improvesfunctional and morphological outcome after cortical contusioninjury in the rat. Acta Neurochirurgica 143(1):73–81. doi:10.1007/s007010170141

McElhaney J, Melvin JW, Roberts VL, Portnoy HD (1973) Dynamiccharacteristics of the tissues of the head. In: Kenedi RM (ed)Perspectives in biomedical engineering. Macmillian Press Ltd,London, pp 215–222

Moore DF, Radovitzky RA, Shupenko L, Klinoff A, Jaffee MS, RosenJM (2008) Blast physics and central nervous system injury. FutureNeurol 3(3):243–250. doi:10.2217/14796708.3.3.243

Moore DF, Jerusalem A, Nyein M, Noels L, Jaffee MS, RadovitzkyRA (2009) Computational biology—modeling of primary blasteffects on the central nervous system. Neuroimage 47:T10–T20.doi:10.1016/j.neuroimage.2009.02.019

Moss WC, King MJ, Blackman EG (2009) Skull flexure from blastwaves: a mechanism for brain injury with implications for helmetdesign. Phys Rev Lett 103:10–108702. doi:10.1103/PhysRevLett.103.108702

Mott DR SD, Young TR, Levine J, Dionne JP, Makris A, Hubler G(Sept 1st–5th 2008) Blast-induced pressure fields beneath a mili-tary helmet. In: 20th international symposium on military aspectsof blast and shock, Oslo

Nahum A, Smith R, Ward C (1977) Intracranial pressure dynamicsduring head impact. In: Proceedings of 21st stapp car crash con-ference, pp 339–366

Nakagawa A, Fujimura M, Kato K, Okuyama H, Hashimoto T, Takay-ama K, Tominaga T (2009) Shock wave-induced brain injury in rat:novel traumatic brain injury animal model Acta NeurochirurgicaSupplements. In: Steiger HJ (ed) Acta neurochirurgica supplemen-tum, vol 102. Springer, Vienna, pp 421–424. doi:10.1007/978-3-211-85578-2_82

National Institutes of Health (2009) The Visible Human Project,National Library of Medicine, http://www.nlm.nih.gov/research/visible/visible_human.html

Nicolle S, Lounis M, Willinger R, Palierne JF (2005) Shear linearbehavior of brain tissue over a large frequency range. Biorheol-ogy 42(3):209–223

Nusholtz GS, Kaiker PS, Gould WS (1987) Two factors critical in thepressure response of the impacted head. Aviat Space Environ Med58(12):1157–1164

Nyein MK, Jason AM, Yu L, Pita CM, Joannopoulos JD, Moore DF,Radovitzky RA (2010) In silico investigation of intracranial blastmitigation with relevance to military traumatic brain injury. ProcNatl Acad Sci. doi:10.1073/pnas.1014786107

Pervin F, Chen WW (2009) Dynamic mechanical response of bovinegray matter and white matter brain tissues under compression.J Biomech 42(6):731–735. doi:10.1016/j.jbiomech.2009.01.023

Prevost TP, Balakrishnan A, Suresh S, Socrate S (2011) Biomechan-ics of brain tissue. Acta Biomaterialia 7(1):83–95. doi:10.1016/j.actbio.2010.06.035

Ramos A, Simões JA (2006) Tetrahedral versus hexahedral finite ele-ments in numerical modelling of the proximal femur. Med EngPhys 28(9):916–924. doi:10.1016/j.medengphy.2005.12.006

Ruan JS, Khalil T, King AI (1994) Dynamic response of the humanhead to impact by three-dimensional finite element analysis. J Bio-mech Eng Trans ASME 116(1):44–50

Schneiders R (2000) Algorithms for quadrilateral and hexahedral meshgeneration. In: Proceedings of the VKI lecture series on computa-tional fluid cynamics

Stalnaker RL (1969) Mechanical properties of the head, Ph.D. Disser-tation. West Virginia University

Sundaramurthy A, Alai A, Ganpule S, Holmberg A, Plougonven E,Chandra N (2012) Blast-induced biomechanical loading of therat: experimental and anatomically accurate computational blastinjury model. J Neurotrauma [ahead of print. doi:10.1089/neu.2012.2413]

Takhounts EG, Eppinger RH, Campbell JQ, Tannous RE, Power ED,Shook LS (2003) On the development of the SIMon finite elementhead model. Stapp Car Crash J 47:107–133

Takhounts EG, Ridella SA, Hasija V, Tannous RE, Campbell JQ,Malone D, Danelson K, Stitzel J, Rowson S, Duma S (2008) Inves-tigation of traumatic brain injuries using the next generation of sim-ulated injury monitor (SIMon) finite element head model. StappCar Crash J 52:1–31

Tanielian T, Jaycox LH (2008) Invisible wounds of war. RAND Corp,Santa Monica

Taylor PA, Ford CC (2009) Simulation of blast-induced early-timeintracranial wave physics leading to traumatic brain injury.J Biomech Eng Trans ASME 131(6):061007. doi:10.1115/1.3118765

Teasdale G, Jennett B (1974) Assessment of coma and impaired con-sciousness: a practical scale. Lancet 304(7872):81–84. doi:10.1016/s0140-6736(74)91639-0

Trosseille X, Tarriére C, Lavaste F, Guillon F, Domont A (1992) Devel-opment of a F.E.M. of the human head according to a specifictest protocol. SAE Technical Paper 922527. In: Stapp car crashconference. doi:10.4271/922527

Wang Y, Wei YL, Oguntayo S, Wilkins W, Arun P, Valiyaveettil M,Song J, Long JB, Nambiar MP (2011) Tightly coupled repetitiveblast-induced traumatic brain injury: development and character-ization in mice. J Neurotrauma 28(10):2171–2183. doi:10.1089/neu.2011.1990

Ward CC, Chan M, Nahum AM (1980) Intracranial pressure—a braininjury criterion. In: Proceedings of 24th stapp car crash conferenceSAE No. 801304, p 161

123


http://dx.doi.org/10.1007/s00193-003-0197-y

http://dx.doi.org/10.1007/s00193-003-0197-y

http://dx.doi.org/10.1007/s11630-000-0042-x

http://dx.doi.org/10.1016/s0021-9290(01)00202-0

http://dx.doi.org/10.1016/s0021-9290(01)00202-0

http://dx.doi.org/10.1111/j.1460-9568.2005.04115.x

http://dx.doi.org/10.1111/j.1460-9568.2005.04115.x




http://dx.doi.org/10.1016/0021-9290(80)90048-2

http://dx.doi.org/10.1016/0021-9290(80)90048-2

http://dx.doi.org/10.1007/s007010170141

http://dx.doi.org/10.1007/s007010170141

http://dx.doi.org/10.2217/14796708.3.3.243

http://dx.doi.org/10.1016/j.neuroimage.2009.02.019

http://dx.doi.org/10.1103/PhysRevLett.103.108702

http://dx.doi.org/10.1103/PhysRevLett.103.108702

http://dx.doi.org/10.1007/978-3-211-85578-2_82

http://dx.doi.org/10.1007/978-3-211-85578-2_82

http://www.nlm.nih.gov/research/visible/visible_human.html

http://www.nlm.nih.gov/research/visible/visible_human.html

http://dx.doi.org/10.1073/pnas.1014786107

http://dx.doi.org/10.1016/j.jbiomech.2009.01.023

http://dx.doi.org/10.1016/j.actbio.2010.06.035

http://dx.doi.org/10.1016/j.actbio.2010.06.035

http://dx.doi.org/10.1016/j.medengphy.2005.12.006



http://dx.doi.org/10.1115/1.3118765

http://dx.doi.org/10.1115/1.3118765

http://dx.doi.org/10.1016/s0140-6736(74)91639-0

http://dx.doi.org/10.1016/s0140-6736(74)91639-0

http://dx.doi.org/10.4271/922527




Wieding J, Souffrant R, Fritsche A, Mittelmeier W, Bader R (2012)Finite element analysis of osteosynthesis screw fixation in the bonestock: an appropriate method for automatic screw modelling. PLoSOne 7(3):e33776. doi:10.1371/journal.pone.0033776

Willinger R, Kang HS, Diaw B (1999) Three-dimensional human headfinite-element model validation against two experimental impacts.Ann Biomed Eng 27(3):403–410. doi:10.1114/1.165

Zhang L, Yang KH, Dwarampudi R, Omori K, Li T, Chang K, HardyWN, Khalil TB, King AI (2001a) Recent advances in brain injuryresearch: a new human head model development and validation.Stapp Car Crash J 45:369–394

Zhang LY, Yang KH, King AI (2001b) Comparison of brain responsesbetween frontal and lateral impacts by finite element modeling.J Neurotrauma 18(1):21–30. doi:10.1089/089771501750055749

Zhang LY, Yang KH, King AI (2004) A proposed injury threshold forintroduction mild traumatic brain injury. J Biomech Eng TransASME 126(2):226–236. doi:10.1115/1.1691446

Zhu F, Mao H, DalCengio Leonardi A, Wagner C, Chou C, Jin X, BirC, VandeVord P, Yang KH, King AI (2010) Development of anFE Model of the rat head subjected to air shock loading. Stapp CarCrash J 54:211–225

Zhu F, Wagner C, DalCengio Leonardi A, Jin X, VandeVord P, ChouC, Yang K, King A (2012) Using a gel/plastic surrogate to studythe biomechanical response of the head under air shock loading:a combined experimental and numerical investigation. BiomechModel Mechanobiol 11(3–4):341–353. doi:10.1007/s10237-011-0314-2

Zoghi-Moghadam M, Sadegh AM (2009) Global/local head models toanalyse cerebral blood vessel rupture leading to ASDH and SAH.Comput Methods Biomech Biomed Eng 12(1):1–12. doi:10.1080/10255840802020420

123


http://dx.doi.org/10.1371/journal.pone.0033776

http://dx.doi.org/10.1114/1.165

http://dx.doi.org/10.1089/089771501750055749

http://dx.doi.org/10.1115/1.1691446

http://dx.doi.org/10.1007/s10237-011-0314-2

http://dx.doi.org/10.1007/s10237-011-0314-2

http://dx.doi.org/10.1080/10255840802020420

http://dx.doi.org/10.1080/10255840802020420

mechanics of blast loading on the head models

Documents